According to a known prior art, containers are removed from a container storage area and sent via a height-adjustable rack serving device, which can be displaced along the container storage area, to a central distribution system, which joins the container storage area. In particular, the rack serving device serves two opposite storage racks over the entire height of the rack (cf. DE 197 12 839 A1). The limited dispatch output and inflexibility of the rack serving system is a disadvantage.